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Numerical Methods

Code: EIC0021     Acronym: MNUM

Classification Keyword
OFICIAL Mathematics

Instance: 2018/2019 - 1S Ícone do Moodle

Active? Yes
Responsible unit: Department of Mining Engineering
Course/CS Responsible: Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEIC 172 Syllabus since 2009/2010 2 - 4,5 56 121,5

Teaching Staff - Responsibilities

Teacher Responsibility
José Manuel Soutelo Soeiro de Carvalho

Teaching - Hours

Lectures: 2,00
Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 1 2,00
José Manuel Soutelo Soeiro de Carvalho 2,00
Recitations Totals 6 12,00
Maria de Lurdes Proença de Amorim Dinis 4,00
Rui Jorge Coelho de Sousa 2,00
José Manuel Soutelo Soeiro de Carvalho 6,00

Teaching language

Suitable for English-speaking students


The course aims at providing the student with solid numerical methods foundations. It is topic oriented, covering numerical error analysis, algebraic and differential equation and systems solving, definite integration, non-linear optimization and curve fitting.

The student will be able to:

  • dentify numerical problems, choosing and implementing the right solution method, after doing numerical experimentation;
  • understand numerical methods in the context of engineering, working on examples from engineering practice;
  • criticise results, from the methodological, implementation and problem context points of view.

Learning outcomes and competences

The student will be able to:

  • Identify numerically solvable  engineering problems;
  • Put forward numerical solutions for a given engineering problem, comparing and choosing appropriate methods;
  • Identify issues in that solution;
  • Criticise results;
  • Implement a reasonably efficient computational solution.

Working method


Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Calculus, Algebra, Introductory Programming.

Familiarity with interactive calculation environments - worksheets, calculators, CAS.



  • Number representation;

  • Numerical error analysis;

  • Roots of equations;

  • Systems of non linear equations;

  • Systems of linear equations;

  • Numerical integration;

  • Ordinary Differential equations;

  • Single and multi-variable unconstrained optimization;

  • Curve fitting.

Mandatory literature

Steven C. Chapra, Raymond P. Canale; Numerical methods for engineers. ISBN: 978-007-126759-5
Carlos Madureira, Cristina Vila, José Soeiro Carvalho; Métodos Numéricos, um curso para o Mestrado Integrado em Engenharia Informática e Computadores da FEUP, 2009 (available in e-learning server)

Complementary Bibliography

Conte, S. D.; Elementary numerical analysis. ISBN: 0-07-012447-7
Dahlquist, Germund; Numerical Methods. ISBN: 0-13-627315-7
Cheney, Ward; Numerical mathematics and computing. ISBN: 978-0-495-11475-8

Teaching methods and learning activities

Classes are computer based, using packages such as Maxima, MatLab and Excel.

Students will also implement computer solutions in their choice programming language.

Working focus will be on precision, efficiency and robustness of computer solutions.

Students will identify, formulate and solve an engineering numerical problem as assignment work.


Linguagem de Programação
The Mathworks - Matlab - Release 11.1
Folha de Cálculo


Physical sciences > Mathematics > Applied mathematics > Numerical analysis
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation Weight (%)
Exame 55,00
Participação presencial 4,50
Teste 40,50
Total: 100,00

Amount of time allocated to each course unit

Designation Time (hours)
Estudo autónomo 70,00
Frequência das aulas 52,00
Total: 122,00

Eligibility for exams

To obtain attendance students may not exceed the maximum number of missed classes, complying with school attendance rules. (attendance registration will be done in every  class).

Calculation formula of final grade

Students will be evaluated by two assessment tests (T1, T2), and a "participation" (P) component, involving several homework problems, attendance and general class intervention.  
They must also attend a final exam. 

The frequency grade is 

NF = (0.1 * P + 0.45 * T1 + 0.45 * T2) 
T1, T2 – Midle tests; 
P - Participation in class. 

The final score after the first call will be calculated as follows: 

NE1 = 0.45* NF +0.55 * NE 

NE1 – Final grade after the first call; 
NF - Distributed evaluation (frequency) grade; 
NE – Exam grade. 

Students who do not pass the 1st call exam can undertake a 2nd call exam. 

The grade after the 2nd call is the highest value obtained by weighting together the exam and the distributed evaluation grades or just the 2nd call exam. 

NER = max (0.45 * NF +0.55 * NR ; NR) 
NER – Final grade after 2nd call; 
NR – 2nd call exam grade; 
NF - Distributed evaluation grade 

Grades over 18/20 will be subject to an oral discussion.


Special assessment (TE, DA, ...)

Students with special status may choose between the normal evaluation mode or "evaluation with final exam", but choice must be comunicated to teachers before the end of september.

Classification improvement

Special global examination.
Grades over 18/20 will be subject to an oral discussion.

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